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ScanSolve AI Answer
To find the time for one revolution (period) and the radius of the circle of a conical pendulum, we use the given information: • Length of the string, L = 100 cm = 1.0 m • Angle with the vertical, = 30^ • We will use the acceleration due to gravity, g = 9.8 m/s^2. Step 1: Calculate the radius of the circle, r. The radius of the circular path is related to the length of the string and the angle by trigonometry. r = L Substitute the given values: r = (1.0 m) (30^) r = (1.0 m) (0.5) r = 0.5 m Converting to centimeters: r = 0.5 m × 100 cm1 m r = 50 cm Step 2: Calculate the time for one revolution (period), T. For a conical pendulum, the period T is given by the formula: T = 2 sqrt((L )/(g)) Substitute the given values: T = 2 sqrt((1.0 m)) (30^)9.8 m/s^2 We know that (30^) = sqrt(3)2 ≈ 0.8660. T = 2 sqrt(1.0 m) × 0.86609.8 m/s^2 T = 2 sqrt((0.8660)/(9.8)) T = 2 sqrt(0.088367... s)^2 T = 2 (0.297266... s) T ≈ 1.8676 s The radius of the circle is 50 cm. The time for one revolution (period) is 1.87 s.